I have a Mitsubishi 1080 Series HDTV big screen not turn the power button TV comes on then TV shuts back off

Hi John

Check the switch mode power supply inside the TV.
Caution.... lethal voltages

The power button is digital these days. That is... it does not have the AC power directly connected to it. Like a normal appliance.
It's a Computer.
Nowadays, the switchmode power supply module converts the incoming AC power to the lower DC voltages required by the other circuit boards.
It uses lots of Electrolytic Capacitors to clean up noise in the DC power. Being Electrolytic they are prone to leaking & bulging so they don't do their job. They won't hold a charge. By pulling the plug and restarting, you have found a way to overcome the problem. But only temporarily. When the Cap goes fully bad, you won't be able to start the TV any more.
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There's a good chance you have failing electrolytic capacitors either in the power section or the inverter section or both.
Any caps in these sections that look bulged at the top, or bulged/leaking at the bottom need to be replaced.
If you repeatedly turn it off and on, eventually it'll probably stay on, but every time you turn it off, the TV will get harder and harder to start up until one day it just won't.
Sometimes you have to do the opposite to start it up and unplug it for some time and then try again.
If you aren't tech savvy, don't worry, read the rest of this solution and watch the videos.
If you are handy with a soldering iron and can identify the power supply and inverter / FM section for the backlights, an inexpensive handful of capacitors will likely fix you right up.
Match the capacitance on the capacitors. Go over voltage if you can, and still have them fit.
IE - it's not a bad idea to replace a 10V cap with a 16V or 25V or even a 50V, but don't replace a 680uF cap with a 500uF or a 1000uF (unless you are positive it's only doing ripple filtering, and even then, you should go OVER, not under the uF rating).
Most of the caps that go are 5v to 25V 1000uF or 3300uF.
Replacement Caps can be slightly higher values (not lower) depending on available space.
Also... a higher temperature rating is beneficial.

See Cap Replacement Here
NOTE: Even when Disconnected from the Mains.... Capacitors on the SwitchMode Power Supply board on the 110vac / 240vac Mains Side....can supply a shock hazard to unwary people.
The DC Side is far safer at 5 to 20v
But... There is no Really High 15 to 25Kv inside Digital TV's any more. So... You don't need to leave TV disconnected for a day to discharge these voltages as stated in the attached video.

Samsung TV Power on Problem Capacitor Replacement

How to Repair Your Plasma TV With Blinking LED

How to Replace an Electrolytic Capacitor